Functional Quantization-Based Data Compression in Seismic Acquisition

The trend in seismic acquisition is geared toward high geophone densities. Future node densities are expected to be on the order of 1M nodes, leading to a huge aggregate data rate in the geophone array and requiring the use of some form of signal compression. This work presents a family of signal compression algorithms based on vector quantization and its transposition to the infinite-dimensional case—functional quantization (FQ). Using FQ, we quantize the entire sample path of the seismic waveform in a target function space, instead of quantizing individual samples. The polynomial design and computational complexity afforded by FQ allow for online training of codebooks where the statistics of the seismic wavefield may be changing. An efficient algorithm for the construction of a functional quantizer is given. It is based on Monte Carlo simulation to circumvent the curse of high dimensionality and avoids explicit construction of Voronoi regions to tessellate the function space of interest. In the sequel, we augment our basic FQ architecture with three different VQ techniques in the literature. The augmentation yields hybridized FQ strategies. These hybrid quantization algorithms are: (1) FQ-classified VQ, (2) FQ-residual/multistage VQ and (3) FQ-recursive VQ. The joint quantizers are obtained by replacing regular VQ codebooks in these hybrid quantizers by their FQ equivalents. Simulation results show that the FQ combined with these different VQ techniques performs better in the rate–distortion sense than either FQ alone or the aforementioned VQ techniques in isolation.